MonographDOI
Mathematical Models in Biology
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TLDR
The theory of linear difference equations applied to population growth and the applications of nonlinear difference equations to population biology are explained.Abstract:
Part I. Discrete Process in Biology: 1. The theory of linear difference equations applied to population growth 2. Nonlinear difference equations 3. Applications of nonlinear difference equations to population biology Part II. Continuous Processes and Ordinary Differential Equations: 4. An introduction to continuous models 5. Phase-plane methods and qualitative solutions 6. Applications of continuous models to population dynamics 7. Models for molecular events 8. Limit cycles, oscillations, and excitable systems Part III. Spatially Distributed Systems and Partial Differential Equation Models: 9. An introduction to partial differential equations and diffusion in biological settings 10. Partial differential equation models in biology 11. Models for development and pattern formation in biological systems Selected answers Author index Subject index.read more
Citations
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Journal ArticleDOI
Single-species Models of the Allee Effect: Extinction Boundaries, Sex Ratios and Mate Encounters
TL;DR: Individual-based models seem to be most capable of explaining mechanisms leading to the Allee effect, and may give better predictions of extinction thresholds than heuristic models but require specific information and are data intensive.
Journal ArticleDOI
Catastrophic vegetation shifts and soil degradation in terrestrial grazing systems.
TL;DR: It has long been recognized that alternative vegetation states may occur in terrestrial grazing systems, but recent studies on semi-arid grasslands and arctic salt marshes relate catastrophic events in these systems to plant-soil interactions.
Journal ArticleDOI
The dynamics of cell cycle regulation
TL;DR: Bifurcation diagrams are a useful analytical tool, providing new views of the dynamical organization of the cell cycle, the role of checkpoints in assuring the integrity of the genome, and the abnormal regulation of cell cycle events in mutants.
Journal ArticleDOI
Alternate stable states and threshold effects in semi-arid grazing systems.
Max Rietkerk,J. van de Koppel +1 more
TL;DR: In this paper, the authors show that the interactions between water infiltration or nutrient retention and plant density potentially give rise to the existence of alternate stable vegetation states and threshold effects in semi-arid grazing systems, even without the effect of a nonlinear herbivore functional response or plant competition.
Journal ArticleDOI
On fractional order differential equations model for nonlocal epidemics
Elsayed Ahmed,A. S. Elgazzar +1 more
TL;DR: A fractional order model for nonlocal epidemics is given and stability of fractional orders equations is studied to be relevant to foot-and-mouth disease, SARS and avian flu.